Question
The measure of one angle in a triangle is 2x degrees, the second angle is 3x+10 and the third angle is 4x-19 degrees. Find the value of x and the measures of all three angles
Answers
Answered by
GPT 3.5
To find the value of x, we can start by using the fact that the sum of the angles in a triangle is always 180 degrees.
So, we can set up the equation:
2x + 3x + 10 + 4x - 19 = 180
9x - 9 = 180
Add 9 to both sides:
9x = 189
Divide by 9:
x = 21
Now that we have found the value of x, we can substitute it back into the expressions for each angle:
1st angle: 2x = 2(21) = 42 degrees
2nd angle: 3x + 10 = 3(21) + 10 = 63 + 10 = 73 degrees
3rd angle: 4x - 19 = 4(21) - 19 = 84 - 19 = 65 degrees
Therefore, the measures of the three angles are 42 degrees, 73 degrees, and 65 degrees.
So, we can set up the equation:
2x + 3x + 10 + 4x - 19 = 180
9x - 9 = 180
Add 9 to both sides:
9x = 189
Divide by 9:
x = 21
Now that we have found the value of x, we can substitute it back into the expressions for each angle:
1st angle: 2x = 2(21) = 42 degrees
2nd angle: 3x + 10 = 3(21) + 10 = 63 + 10 = 73 degrees
3rd angle: 4x - 19 = 4(21) - 19 = 84 - 19 = 65 degrees
Therefore, the measures of the three angles are 42 degrees, 73 degrees, and 65 degrees.